Answer:
h'=0.25m/s
Explanation:
In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).
So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of 
. As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:
notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.
If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:
When solving for r, we get:
so we can substitute this into our volume of a cone formula:
which simplifies to:
So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:
Which simplifies to:
So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)
So we get:
Now we can substitute the provided values into our equation. So we get:
so:
Answer:
D = -4/7 = - 0.57
C = 17/7 = 2.43
Explanation:
We have the following two equations:
First, we isolate C from equation (2):
using this value of C from equation (3) in equation (1):
<u>D = - 0.57</u>
Put this value in equation (3), we get:
<u>C = 2.43</u>
Here, you can calculate it's potential energy with respect to ground.
We know, U = mgh
Here, m = 75 Kg
g = 9.8 m/s² [ constant value for earth system ]
h = 300 m
Substitute their values into the expression:
U = 75 × 9.8 × 300
U = 220500 J
In short, Your Final Answer would be 220,500 J
Hope this helps!
Answer:
The main physical characteristics of matter are mass, volume, weight, density, odor, and color. These are the characteristics that help us to see matter, feel matter, and taste matter.
Explanation:
Answer:
The correct answer is - C) Jackie may maintain healthy body fat levels.
Explanation:
Jackie has a very active daily and on weekends routine that includes riding the bike, playing volleyball, pushing weeds, and sweeping the porch. The activities that Jackie is performing daily as well as the time that she spends on exercise may help her to maintain body fat levels.
Being physically active helps in maintaining fat levels in the body of an individual, and it is healthy for the individual.
Thus, the correct answer is - C) Jackie may maintain healthy body fat levels.
